利用理论和数值方法研究了Kagome螺旋波导阵列的拓扑绝缘体特性。Kagome晶格的时间反转对称性被螺旋性打破，形成光子拓扑绝缘体。为了验证螺旋度引起的拓扑相变，我们计算了带结构的Berry曲率和Chern数，也证明了边缘态在某些动量值的单向传播和拓扑保护性质。有趣的是，相同的Kagome螺旋波导阵列，可以支持具有不同动量沿同一边界传播但方向相反的拓扑边缘态。

      图1. kagome的螺旋波导阵列

Results in Physics 12 (2019) 996–1001

Topological insulator properties of photonic kagome helical waveguide arrays

Hua Zhong, Rong Wang and Yiqi Zhang

References

[1] Hasan MZ, Kane CL. Colloquium: topological insulators. Rev Mod Phys

2010;82:3045–67.

[2] Qi X-L, Zhang S-C. Topological insulators and superconductors. Rev Mod Phys 2011;83:1057–110.

[3] Yang Z, Gao F, Shi X, Lin X, Gao Z, Chong Y, et al. Topological acoustics. Phys Rev Lett 2015;114:114301.

[4] He C, Ni X, Ge H, Sun X-C, Chen Y-B, Lu M-H, et al. Acoustic topological insulator and robust one-way sound transport. Nat Phys 2016;12:1124–9.

[5] Huber SD. Topological mechanics. Nat Phys 2016;12:621–3.

[6] Jotzu G, Messer M, Desbuquois R, Lebrat M, Uehlinger T, Greif D, et al.

Experimental realisation of the topological Haldane model. Nature 2014;515:237–40.

[7] Leder M, Grossert C, Sitta L, Genske M, Rosch A, Weitz M. Real-space imaging of a topologically protected edge state with ultracold atoms in an amplitude-chirped optical lattice. Nat Commun 2016;7:13112.

[8] Beeler MC, Williams RA, Jiménez-García K, LeBlanc LJ, Perry AR, Spielman IB. The spin Hall effect in a quantum gas. Nature 2013;498:201–4.

[9] Kennedy CJ, Siviloglou GA, Miyake H, Burton WC, Ketterle W. Spin-orbit coupling and quantum spin hall effect for neutral atoms without spin flips. Phys Rev Lett 2013;111:225301.

[10] Haldane FDM, Raghu S. Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry. Phys Rev Let 2008;100:013904.

[11] Wang Z, Chong Y, Joannopoulos JD, Soljacic M. Observation of unidirectional backscattering-immune topological electromagnetic states. Nature 2009;461:772–5.

[12] Lindner NH, Refael G, Galitski V. Floquet topological insulator in semiconductor quantum wells. Nat Phys 2011;7(6):490–5.

[13] Khanikaev AB, Mousavi SH, Tse W-K, Kargarian M, MacDonald AH, Shvets G. Photonic topological insulators. Nat Mater 2012;12:233–9.

[14] Chen W-J, Jiang S-J, Chen X-D, Zhu B, Zhou L, Dong J-W, et al. Experimental realization of photonic topological insulator in a uniaxial metacrystal waveguide. Nat Commun 2014;5:5782.

[15] Dong J-W, Chen X-D, Zhu H, Wang Y, Zhang X. Valley photonic crystals for control of spin and?topology. Nat Mater 2016;16:298–302.